Sure. File an IFR flight plan to wherever you want to start your first approach, then fly the missed approach procedure for that approach. When you declare 'missed approach' ATC will ask you your intentions and then you just tell them you would like to proceed to XXX and fly an approach there (or even, fly a specific approach there). For the sequence of airports you've asked about, just file KWHP - KVNY. After the missed at KVNY tell ATC you want to fly an approach into KBUR and you'll get vectored (out toward SILEX if you're going to shoot the KBUR Rwy 8 ILS). The missed approach procedure for the KBUR ILS takes you back toward VNY which is the IAF for the KWHP VOR-A approach, so it all kind of works.
Given the proximity of those three airports, be prepared for a simply massive workload. I'd strongly encourage you to work your way up to the sequence you've just described by (for example) flying KWHP - KVNY, missed, KBUR and see how you do with just a single missed-and-divert situation.
-M.
Mark Hargrove Longmont, CO
PE: N757SL (Cessna 182T 'Skylane'), N757SM (Cessna 337 'Skymaster'), N757BD (Beech Duke Turbine)